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Unformatted text preview: Winter 2010 Math 255 Problem Set 11 Due Tuesday 30 March Section 16.7: 16, 26, 40, 44 Section 16.8: 6, 14, 26, 38 Section 16.9: 6, 8, 16, 24 Challenge Problems : ai) Let f = r α , where r 2 = x 2 + y 2 or r 2 = x 2 + y 2 + z 2 . Recall the definition of an improper integral. For what α does: 1. R R U f d A exist when U = { ( x, y )  x 2 + y 2 ≤ 1. 2. R R U f d A exist when U = { ( x, y )  x 2 + y 2 ≥ 1. 3. R R R U f d V exist when U = { ( x, y, z )  x 2 + y 2 + z 2 ≤ 1. 4. R R R U f d V exist when U = { ( x, y, z )  x 2 + y 2 + z 2 ≥ 1. aii) Discuss your results in light of Fubini’s theorem (be sure to state the version of Fubini’s theorem you refer to and where you found it). b) Suppose that R R R U f d V = 0 for all regions U ∈ R 3 . Suppose f is continuous. Explain why f = 0. c) A class is graded on a curve. It is assumed that the class is a representative sample of the population, the probability density function for the numerical score x is 1 Winter 2010 Math 255...
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This note was uploaded on 12/31/2011 for the course MATH 255 taught by Professor Jackwaddell during the Fall '08 term at University of Michigan.
 Fall '08
 JackWaddell
 Math

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